In order to satisfy the demand for higher bit rate optical transmission, for example 40 Gbits/s, a number of non-binary encoding schemes are considered such as Quadrature Phase Shift Keying (QPSK), Differential Quadrature Phase Shift Keying (DQPSK), or Duobinary. External modulators constructed on z-cut lithium niobate are attractive for their lower drive voltage requirements and larger bandwidth capabilities. But z-cut modulators have an asymmetric structure that causes chirp, that is, the ratio between residual phase modulation and the intensity modulation generated. Prior art external modulators in lithium niobate have offered zero chirp within narrow frequency limitations. But over the broader frequency range of high bit rate transmission, the frequency dependence reveals an unacceptably high chirp for non-binary encoding schemes.
FIG. 1 shows a simple prior art Mach-Zehnder (MZ) modulator 10 made in a z-cut lithium niobate substrate 12, having an optical input 14 and output 16, two y-junctions 18, 18′ for splitting and combining light, respectively, and two waveguides 20, 22 of length, L, that make up the arms of the Mach-Zehnder. A signal electrode 24 having an RF input 2 and an RF output 4, and two ground electrodes 26 apply an electric field to the two waveguides 20, 22 in the MZ 10. The RF signal electrode 24 is much narrower than the ground electrodes 26, hence the electric field is much more focused underneath the signal electrode 24, causing an imbalance in the strength of modulation in the two arms of the MZ. For typical electrode designs, the modulation in the waveguide 20 underneath the ground electrode 26 is approximately ⅙th of the modulation of the waveguide 22 under the signal electrode 24. The relative modulation strength, EOi, is defined to be ratio of the modulation in the ith waveguide to the total modulation needed to switch the modulator output from on to off. EO1 and EO2, corresponding to the waveguides 22, underneath the signal 24 and ground 26 electrodes, respectively, are 0.85 and 0.15.
FIG. 2 shows the chirp parameter as a function of frequency. The chirp parameter, α is defined by Equation 3 from F. Koyama and K. Iga, “Frequency chirping in external modulators,” IEEE Journal of Lightwave Technology,” Vol. 6, No. 1, January 1988, pp. 87-93, which can be rewritten in the form
                    α        =                                            ⅆ              ϕ                                      ⅆ              t                                                          1                              2                ⁢                                                                  ⁢                I                                      ⁢                                          ⅆ                I                                            ⅆ                t                                                                        (        1        )            where φ is the net optical phase modulation output by the modulator and I is the intensity of light exiting the modulator. Chirp is referred to as the alpha (α) parameter, which should not be confused with α used to describe the RF loss in an RF electrode. In this application, the chirp parameter is referred to simply as “chirp” to avoid confusion with RF loss.
The chirp is constant but non-zero in FIGS. 2A and B. Depending on which quadrature point of the Mach-Zehnder is chosen as the bias point, the slope of intensity vs. drive voltage can either be positive or negative, causing the calculated chirp value from Equation 1 to be either +0.7 as shown in FIG. 2A or −0.7 shown in FIG. 2B. In all graphs of chirp that follow, it is assumed that the quadrature point corresponding to a chirp value of +0.7 is chosen, for the purpose of defining chirp according to Equation 1.
A prior art modulator with a more complex architecture is shown in FIG. 3. The Dual Parallel Mach-Zehnder (DPMZ) Interferometer 30 has two simple Mach-Zehnder Interferometers 32, 34 nested in the arms of a larger Mach-Zehnder Interferometer 36. This modulator 30 is sometimes used for Quadrature Phase Shift Keying (QPSK) or Differential Quadrature Phase Shift Keying (DQPSK) transmission at 40 Gb/s. There are two independent RF signal electrodes 38A and 38B for the “inner MZ's” 32, 34 and bias electrodes 40 for the larger “outer” MZ 36. Not shown are bias electrodes in the inner MZ's 32, 34, which typically follow the RF signal electrodes 38A and 38B. Note that an x-cut lithium niobate electrode configuration is shown, where the waveguides 31, 33 are positioned between signal 38A and 38B and ground 39 electrodes. This configuration has balanced modulation in the two arms 31, 33 of the inner MZ's resulting in zero chirp for the inner MZ's 32, 34. Another configuration uses z-cut substrate and electrode configuration along with the invention, which permits zero chirp operation. In such a configuration, the waveguides of the inner MZ are underneath the signal and ground electrodes.
In one version of a QPSK system, the two inner MZ's 32, 34 are biased at null while the outer MZ 36 is biased at quadrature as disclosed by T. J. Schmidt, et. al., “Spectrally efficient and impairment-robust modulation techniques for 40 Gb/s optical transmission systems,” NFOEC 2002, Dallas, Tex. A 40 Gb/s signal is split into two 20 Gb/s signals with an encoder. The two 20 Gb/s digital signals are fed into the two RF signal electrodes of the DPMZ. The two modulation signals create optical modulation signals that are orthogonal to one another in optical phase. These two transmitted signals are often referred to as I and Q signals. These two optical signals can be detected independently of one another using a coherent receiver which mixes the received optical signal with a signal from a local oscillator. FIGS. 4A and B show simulation results for the two received signals corresponding to the I and Q transmitted signals in the absence of any chromatic dispersion or other degradation caused by the optical fiber. Note that the two signals are free of distortion.
One problem with the zero-chirp x-cut lithium niobate modulators is the requirement for a higher drive voltage than can be implemented using chirped z-cut lithium niobate modulators. For example, by implementing ridge waveguides in z-cut modulators as described in K. Noguchi, et. al., “Millimeter-wave Ti:LiNbO3 optical modulators,” IEEE Journal of Lightwave Technology, Vol. 16, No. 4, April 1998, pp. 615-619, the drive voltage can be reduced significantly. However, conventional chirped z-cut Mach-Zehnders are unsuitable for use in a DPMZ architecture, as the chirp would severely compromise the orthogonality of the I and Q signals.
Prior art methods for converting a chirped z-cut modulator into a zero-chirp modulator are described in U.S. Pat. Nos. 6,501,867, 7,058,241, 7,088,875, and in the publication literature N. Courjal, et. al., “LiNbO3 Mach-Zehnder modulator with chirp adjusted by ferroelectric domain inversion,” IEEE Photonics Technology Letters, Vol. 14, No. 11, November 2002, pp. 1509-1511. Such designs are desirable to allow for reduced drive voltage available with z-cut lithium niobate technology. While many of the designs are adequate for conventional On-Off Keying (OOK) transmission, they introduce some performance penalty for QPSK transmission due to the residual chirp. There are other transmission formats that require zero-chirp modulators, as well, for example, duobinary.
Electro-optic external modulators made of lithium niobate or lithium tantalite, or electro-optic polymer can be subjected to poling to reverse the crystal structure. Other external modulators are manufactured in semiconductor material such as InP or GaAs.
FIG. 5 shows a prior art single drive z-cut lithium niobate modulator 50 having a two-section MZ 52. The ferroelectric domain has been inverted in section 57 while section 55 is in the original state and the signal electrode 56 moves from waveguide 53 to waveguide 51 in the domain inverted section 57. The sections are defined by the lengths L1 and L2, shown by dashed lines, where the signal electrode 56 overlaps alternate waveguides 51, 53. Throughout this application the labels L1 to LN for the lengths of the N sections are used such that L1 is disposed closest to the RF input 2, and LN is disposed closest to the RF output 4. The electrode 56 cross-over portion is not included in the section length. The two ground electrodes adjacent to the signal electrode 56 are not shown for ease of illustration. The alternating electrode path 56 reverses the asymmetric structure when the domain is reversed in order to preserve the polarity of the accumulated modulation. If the two sections 55, 57 have equal length, chirp is zero at low frequency, but becomes non-zero at higher frequencies, due to RF loss in the electrode 56 that reduces the signal voltage at the beginning of the second section 57 relative to the first section 55. One can partially compensate for the RF loss by making the length L2 of the second section 57 longer than the length L1 of the first section 55. FIG. 6 shows chirp as a function of frequency for such a design, where lengths L1 and L2 normalized to the total length of the MZ are 0.42 and 0.58, respectively. The modulator is assumed to be velocity-matched, that is the optical and RF velocities are the same. The RF loss in the RF electrode is given by Equation 2, where the assumed values of a00 and a01 are 0.0 Nepers/(cm-(GHz)) and 0.0311 Nepers/(cm-(GHz)0.5), respectively, and L equals 5 cm. The assumed values of a00 and a01 correspond to 0.0 dB/(cm-(GHz)) and 0.27 dB/(cm-(GHz)0.5), respectively. The values in units of dB must be converted to Nepers by multiplying ln(10)/20, before inserting into Equation 2 and all following equations.α(f)L=(α00f+α01√{square root over (f)})L  (2)
For this two-section modulator 50, chirp is about −0.1 at low frequency, is zero at about 18 GHz, and increases to about +0.06 at 40 GHz. Note that the choice of lengths that produce zero chirp at 18 GHz are different if the coefficients defining RF loss are different.
FIGS. 7A and B show simulation results of the received I and Q signals for the case that the two section MZ 52 is used as the inner MZ's 32, 34 of a DPMZ 30 (as in FIG. 3). There is distortion in the signals. The distortion is due to crosstalk between the two 20 Gb/s bit streams caused by the residual chirp. FIGS. 8A and B show the simulated crosstalk in the two received bitstreams. In these simulations, the I signal at the transmitter is turned off, and the resulting received I signal is calculated. Similarly, the received Q signal is calculated for the case where no Q signal is transmitted. Ideally, the two signal amplitudes should always be zero, but are non-zero due to the transmitted I and Q signals not being completely orthogonal to one another. The amplitude of the crosstalk signals are on the order of 10% to 12% of the amplitude of the main signal.
A prior art three section single drive MZ modulator 60 is shown in FIG. 9, as taught in U.S. Pat. Nos. 7,058,241 and 7,088,875 assigned to Fujitsu Limited. As disclosed in one embodiment, the domain inverted section L2 is centered along the length of the MZ 60, and L1 is equal to L3. In addition, the total length of the uninverted sections (L1+L3) is equal to the length of the inverted section (L2). The normalized lengths L1, L2, and L3 are 0.25, 0.50, and 0.25, respectively. RF signal electrode 66 is disposed over waveguide 63 at RF input 2 in section L1 and crosses to waveguide 61 in section L2 over the domain inverted section 67 and returns to waveguide 63 in section L3 where it is coupled to the RF output 4.
FIG. 10 shows the chirp vs. frequency plot for the prior art three-section MZ 60 with centered domain inversion section. Residual chirp is much lower than for the two-section design. Chirp is zero at low frequency and steadily increases to about 0.02 at 40 GHz. FIGS. 11A and B show crosstalk in the I and Q signals for a 40 Gb/s QPSK system. The amplitude of the crosstalk is only about 1% of the main signal. This cross-talk is a consequence of the chirp shown in FIG. 10, showing that the I and Q orthogonal signals are not completely independent due to the chirp. This level of crosstalk may be adequate for 40 Gb/s QPSK, however, there may be some small yet significant performance penalty associated with this crosstalk. There may be other performance issues related to small amounts of residual chirp.
FIGS. 12-18 describe the performance of a prior art three-section MZ 60 for cases where the device parameters are slightly different from the optimal design. It is important that any design be relatively insensitive to variation in device parameters that are likely to occur in manufacture.
FIGS. 12 and 13 show chirp vs. frequency for a prior art three-section MZ 60 with +0.05 and −0.05 velocity walk-off (ΔNRF) between RF and optical signals, respectively. The velocity walk-off value refers to the difference between the optical and microwave indices. Note that the residual chirp increases to a larger value of 0.04 at 40 GHz for either case. FIGS. 14A and B show the simulated crosstalk in the received I and Q signals for the prior art three-section MZ with +0.05 velocity walk-off. The crosstalk amplitude increases to about 2% to 3% of the main signal for this case.
FIGS. 15 and 16 show the chirp vs. frequency for a prior art three-section MZ with 20% higher and 20% lower a01, respectively, while FIGS. 17 and 18 show similar plots where the intrinsic chirp parameter is 0.8 and 0.6, respectively, instead of 0.7. Intrinsic chirp refers to the chirp for the same MZ geometry as a single section without domain inversion. This typically ranges from 0.5 to 1.0 depending on the MZ geometry. Note that changes to RF loss or intrinsic chirp only produce a minor change to the resultant chirp at any frequency from DC to 40 GHz.
FIG. 19 describes a prior art four-section MZ 70, where all the sections are of equal length, as taught in FIGS. 2 and 3 of U.S. Pat. No. 6,501,867 assigned to Lucent Technologies Inc. RF signal electrode 76 is coupled from RF input 2 over waveguide 73 in section L1, and section L3 and alternates over waveguide 71 in the domain inverted regions 77 for sections L2 and L4. Those figures show two-section and seven-section MZ designs, where all the section lengths are equal. The text does not teach a specific length for the sections. FIG. 3 in N. Courjal, et al., referenced above, shows chirp as a function of frequency for a two-section MZ for five different choices of length. The choice closest to zero chirp is the one where the two lengths are equal to one another.
FIG. 20 shows chirp vs. frequency for a prior art four-section MZ 70 where L1=L2=L3=L4 as shown in FIG. 19. Chirp is zero at low frequency, but increases to >0.08 at 40 GHz.
FIGS. 21A and B show crosstalk in the I and Q signals for the prior art four-section MZ 70, for a 40 Gb/s QPSK system. Simulations assume a structure similar to FIG. 3, where each of the smaller MZ's within the structure contain a four-section zero-chirp MZ. The amplitude of the crosstalk is as much as 6% of the main signal, which is likely to have some impact on system performance. The high amount of residual chirp may introduce other system penalties.
Accordingly, a low voltage external optical modulator that can provide a constant chirp versus frequency response remains highly desirable; particularly an external single drive optical modulator suitable for non-binary encoding schemes is desired.